Grade 8 Math Instructional Materials 2013.pdf - RPDP

Nevada 

DEPARTMENT 

OF 

EDUCATION 

GRADE 

8 

Instructional 

Materials 

for the 

CRITERION 

REFERENCED 

TEST 

Nevada 

Grade 8 

MATHEMATICS 

Copyright © 2013 by the Nevada Department of Education

JAMES W. GUTHRIE 

Superintendent of 

Public Instruction 

RORIE FITZPATRICK 

Deputy Superintendent 

Instructional, Research, and 

Evaluative Services 

STATE OF NEVADA 

TEACHER LICENSURE 

SOUTHERN NEVADA OFFICE 

9890 S. Maryland Parkway 

Suite 221 

Las Vegas, Nevada 89183 

(702) 486-6458 

Fax: (702) 486-6450 

DEBORAH CUNNINGHAM 

Deputy Superintendent 

Administrative and 

Fiscal Services 

Dear Educators, 

DEPARTMENT OF EDUCATION 

700 E. Fifth Street 

Carson City, Nevada 89701-5096 

(775) 687-9217 · Fax: (775) 687-9101 

www.doe.nv.gov 

SATELLITE OFFICE 

ADDRESSES/MAPS 

http://www.doe.nv.gov 

The following materials, developed as a collaborative effort between the Nevada Department of Education and 

WestEd, a nonprofit research, development, and service agency, are designed to be used as part of a guided 

instructional activity to support student performance on items aligned to the Common Core Standards. 

We have provided p-values (the proportion of students who got the item correct) for the multiple-choice items 

that were field tested in the 2011-2012 administration. The p-values indicate how students performed on the 

items. In addition, we are providing the percentage of students selecting each response option. The p-values, 

combined with the item-level percentages by response option, provide valuable data to the field as to what types 

of errors students are making. For mathematics, no p-value is reported if that item did not appear on the field 

test. In mathematics, some field test items have been used as a model to mirror the content being assessed and 

therefore the p-values are based on the field test version of the item and not the actual item as it appears in these 

materials. These items are indicated by an asterisk. To further understanding of constructed-response items, 

scoring guides and annotated student examples have been included. 

While these materials can provide students with practice in answering assessment items, we believe it is critical 

that these materials be used to help students understand the elements of the state assessment and guide them in 

the use of effective strategies that will support their ability to comprehend and take a variety of assessments. If 

you choose, however, to use these support documents solely as a practice activity, we highly recommend that 

you go back over each item with students and investigate each response to better understand their knowledge of 

the assessment. 

Vocabulary Knowledge 

The Nevada Department of Education believes that students are not thoroughly being taught the content 

vocabulary of the Nevada Mathematics Content Standards. For example, equation, expression, coordinate, 

function, histogram, analyze, and justify are terms used in the assessments at grade-appropriate levels. 

Students in Nevada, therefore, must have repeated experiences with speaking, listening, reading, and writing 

the vocabulary of the standards. Students should be able to use the vocabulary of the standards when they are 

engaged in classroom discussion, read them in assessments, and effectively use the vocabulary in their writing. 

Types of Questions and Support Documents 

The mathematics assessment includes two types of questions—multiple-choice questions for all grades (3 – 8 

and high school) and constructed-response questions for grades 4 – 8. 

Copyright © 2013 by the Nevada Department of Education 

Page i

To help prepare students for constructed-response questions, we have provided you with: 

1. the student checklist (included in the student test booklet at grades 4 and 5) 

2. the general student rubric (included in the student test booklet at grades 6 – 8) 

3. item-specific rubrics 

4. annotated student work 

With the use of these materials, students can become familiar with the different types of questions used on the 

state and future assessments. They can learn to use the checklist or rubric to determine if they have answered 

the constructed-response questions completely. Familiarity with the tools provided as part of the assessment and 

the vocabulary of the standards can result in less anxiety on the part of students and teachers. (Please note that 

the student checklist and general rubric can be on the walls of your classroom throughout the school year. As 

you assign constructed-response questions, students can use these tools as they develop their answers.) 

Depth of Knowledge (DOK) Levels - In addition to measuring a broad spectrum of mathematics content 

domains, the types of questions included in these instructional materials allow for the assessment of different 

levels of cognitive complexity. The Nevada Proficiency Examination Program in mathematics includes items 

to assess three Depth of Knowledge levels. These DOK levels are based on descriptions developed by Dr. 

Norman Webb and adapted for Nevada's mathematics assessments. We suggest that you engage students in 

question writing so they not only can recognize these levels of complexity, but can begin to formulate them as 

well. The following are the three DOK levels used on Nevada’s mathematics assessments: 

DOK Level 1: Recall - Level 1 requires the recall of facts or use of basic skills. A level 1 item consists of 

literal recall from text, paraphrasing, or simple understanding of a single word or phrase. A level 1 item 

may require a simple connection between sentences, which may be considered a very basic inference. 

DOK Level 2: Use of Concepts and Skills - Level 2 requires comprehension and mental processing of 

text or portions of text. A level 2 item includes the engagement of some mental processing beyond 

recalling or reproducing a response. A level 2 item requires the application of skills and concepts. Some 

important concepts are covered but not in a deeply complex way. 

DOK Level 3: Strategic Thinking and Problem Solving - Level 3 requires abstract reasoning, critical 

thinking, and/or the application of abstract concepts to new situations. 

We hope that interaction with these instructional support materials will lead to lowered anxiety and better 

understanding of the assessment task that is being presented to students. If you have questions about the 

mathematics materials or how to embed this information into your curriculum, please contact Tracy Gruber at 

tgruber@doe.nv.gov. 

Cindy Sharp 

Nevada Department of Education 


Page ii

Name: 

Mathematics 


This booklet contains mathematics questions for you to answer. There are two types of questions in this 

booklet. For the multiple-choice questions, you will be given four answer choices—A, B, C, and D. You are 

to choose the correct answer from the four choices. Each question has only one right answer. The writtenresponse 

question requires you to give a written response to a question as indicated in the booklet. You 

will be given a separate sheet of paper to answer this question. 

You may use the rubric below to help you do a good job when you are answering the written-response 

question. 

Score 

Full Credit 

Expectation 

Your response addresses all parts of the question clearly and correctly. You use 

and label the proper math terms in your answer. 

Your response shows all the steps you took to solve the problem. 

Partial Credit 

Your response addresses most parts of the question correctly. 

Your response does not show all of your work or does not completely 

explain the steps you took to solve the problem. 

Minimal Credit 

Your response addresses only one part of the question correctly and explains 

the steps you took to solve that one part. In answering the remaining parts of 

the question, your response is incomplete or incorrect. 

Your response does not show all of your work or does not explain all of the 

steps you took to solve the problem. 

No Credit 

Your response is incorrect. 


Page 1

Grade 8 Mathematics 

Instructional Materials 

■ 1 The decimal form of each of four different 

numbers contains an infinite number of 

digits. Stacy writes only the first seven 

digits of each number, without rounding. 

Which of these numbers is most likely to 

be irrational? 

■ 3 3 

What is 216 

A 6 

B 24 

C 36 

D 72 

? 

A 4.090909 

B 4.125000 

C 4.222222 

D 4.898979 

■ 2 Look at the values shown below. 

π 2 38 

99 

7 

3 15 

■ 4 Which is closest to the sum of 1.128 × 10 8 

and 7.282 × 10 7 ? 

A 1.86 × 10 7 

B 8.41 × 10 7 

C 1.86 × 10 8 

D 8.41 × 10 8 

What is the order of the values from 

greatest to least? 

A 

B 

99 

7 

99 

7 

C 3 15 38 

D 3 15 

38 3 15 

2 

π 

2 

3 15 π 38 

99 

7 

2 

π 

99 

7 

2 

π 

38 

Copyright © 2013 by the Nevada Department of Education Page 2 

Go On



■ 5 Look at the equation below. 

3 

10 y − 8 7 6 4 1 2 

y + = + y − 

2 

What is the solution of the equation? 

A y = 2 7 9 

B y = 21 

29 

C y = -1 2 7 

D y = -2 1 5 

■ 6 Which equation does not describe a 

linear function? 

A y = 7 

2 

B y = 2x 

− 5 

C 2y 

= 3x 

− 9 

D 4x 

− 6y 

= 13 

■ 7 Polygon MNPQ is shown on the coordinate 

plane below. A dilation with center of 

dilation at the origin will be performed on 

the polygon. 

M 

-16 -12 

P 

-8 

Q 

16 

12 

8 

4 

-4 

-4 

-8 

-12 

-16 

y 

4 8 12 16 

The location of vertex M after the dilation 

is (-8, 6) . What is the location of vertex N 

after the dilation? 

N 

x 

A (0, 4) 

B (1, 2) 

C (4, 5) 

D (16, 4) 


Go On



■ 8 Jenny used three squares to make a design. She labeled each square with its area. Jenny drew the 

squares so that triangle ABC was formed, as shown in the diagram below. 

A 

169 cm 2 

25 cm 2 144 cm 2 

C 

B 

Jenny uses the converse of the Pythagorean theorem to write a statement about triangle ABC . 

Which statement could Jenny have written? 

A Since triangle ABC is a right triangle, the sum of the length of side AC and the length of side CB 

is equal to the length of side AB . 

B Since triangle ABC is a right triangle, the sum of the area of the square with side AC and the area 

of the square with side CB is equal to the area of the square with side AB . 

C Since the sum of the length of side AC and the length of side CB is equal to the length of 

side AB, the longest side of triangle ABC, then triangle ABC is a right triangle. 

D Since the sum of the area of the square with side AC and the area of the square with side CB is 

equal to the area of the square with side AB, the longest side of triangle ABC, then triangle ABC 

is a right triangle. 


Go On


■ 9 A rectangular prism is shown in the 

diagram below. 

N 

R 

24 mm 

J 

P 

M 

Q 

32 mm 

K 

9 mm 

L 

What is the length of the line segment that 

extends between vertex K and vertex R ? 

■ 


10 

The locations of point A and point B on 

a coordinate plane are described by the 

ordered pairs listed below. 

A(-3, 5) B(2, -1) 

What is the shortest distance between 

point A and point B ? 

A 

B 

C 

D 

11 units 

37 units 

61 units 

73 units 

A 65 mm 

B 40 mm 

C 41 mm 

D 6912 mm 


Go On



Write your answer to Question 11 on a separate sheet of paper. Be sure to answer 

Parts A and B. 

■ 

A bake shop makes a cake shaped like a hemisphere, as pictured below. 

11 

6 in 

cake 

A What is the volume, in cubic inches, of the cake? Leave your answer written in terms of π . 

Show your work. 

B The bake shop also makes a cake shaped like a cylinder. This cake has the same volume and 

radius as the cake from Part A. What is the height, in inches, of the cake shaped like a cylinder? 

Show your work or explain your thinking 


Go On



You may want to go back and check your answers or answer questions 

you did not complete. 

Copyright © 2013 by the Nevada Department of Education Page 7

Nevada 

DEPARTMENT 

OF 

EDUCATION 

GRADE 

8 

Appendix I 

Scoring 

Support 


Nevada 


MATHEMATICS 


Page 8

Item 

Number 

Correct Answers for Multiple-Choice Items 

Item Level Data 

Percentage of Students Selecting 

a Given Response 

Strand DOK P-value A B C D 

1 1 1 0.29 18% 18% 35% 29% ✓ 

2* 1 2 0.23 27% 23% ✓ 17% 33% 

3* 1 1 0.23 23% ✓ 31% 15% 31% 

4 1 1 0.25 10% 24% 25% ✓ 41% 

5* 2 1 0.32 21% 24% 23% 32% ✓ 

6 2 1 0.21 47% 21% ✓ 13% 20% 

7* 4 2 0.22 13% 20% 22% ✓ 45% 

8 4 2 0.23 23% 32% 22% 23% ✓ 

9* 4 2 0.26 21% 33% 26% ✓ 20% 

10 4 2 0.22 46% 26% 22% ✓ 6% 

P-value is the proportion of students who got 

the item correct 

✓ = Correct Answer 

*This is an item that was developed for these 

Instructional Materials, and it mirrors content 

assessed from an item field tested in the 

2011-2012 test administration. The p-value 

and percentages reported here are based on 

the p-value and percentages of the item from 

the 2011-2012 field test. 

Detailed objectives for Content Standards and Depth of Knowledge (DOK) descriptions 

can be found on the Nevada Department of Education web site. 


Nevada 8 2011-12 


Version 6 #50 I-Ref #: WE: Y12_MA2918 Rpt Cat(s): NO NV MATCH 

Date: 1/24/12 

CCCS: 8.G.9 

Score 

Description 

3 Student scores 3 points. 

2 Student scores 2–2.5 points. 

1 Student scores 0.5–1.5 points. 

0 Student’s response provides insufficient evidence of appropriate skills or 

knowledge to successfully accomplish the task. 

Blank No student response. 

Score Points 

Part A: score 1.5 points correct answer with correct and complete work 

OR 

score 1.0 point 

OR 


correct answer with incomplete work 

OR 

incorrect answer due to calculation error (work must be 

shown) 

correct answer with no work 

OR 

some correct procedure 

Part B: score 1.5 points correct answer (based on answer to Part A) with correct 

and complete work or explanation 

OR 


OR 


correct answer (based on answer to Part A) with 

incomplete work or explanation 

OR 

incorrect answer due to calculation error (work must be 

shown) 

correct answer (based on answer to Part A) with no work 

or explanation 

OR 

some correct procedure 

OR 

vague explanation only 


Page 10

Nevada 8 2011-12 


Version 6 #50 I-Ref #: WE: Y12_MA2918 Rpt Cat(s): NO NV MATCH 

Date: 1/24/12 

CCCS: 8.G.9 

Correct Answers 

Part A: 144π (cubic inches) 1 ⎛ 4 

V = πr 

2 ⎝ 3 

2 3 

V = π( 6 ) 

⎞ 

⎠ 

3 

2 

V = π( 216) 

3 

V = 144π 

or equivalent work 

3 

Part B: 

4 (inches) 

2 

V = πr h 

( ) 

144π = π 6 h 

144 = 36h 

4 = h 

or equivalent work 

OR 

2 

Set the two volumes equal to each other and then solve for the 

height. The height of the cake is 4 inches since 144 ÷ 36 = 4 . 


Page 11

Nevada 

DEPARTMENT 

OF 

EDUCATION 

Student 

Response 

Examples by 

Score Point 


Page 12

Contract: 1378 1 Booklet: 1850003573 Page: 1 of 1 Score: 3 RespCode: MA06050 

Annotation: a-1.5 b-1.5 = 3.0 points 

Score Point: 3 

The response to Part A includes a correct answer Anchor and complete work (1.5). The 

Page 1 

response to Part B includes a correct answer and complete work/explanation (1.5). 


Page 13


Annotation: a-1.5 b-1.5 = 3.0 points 


The response to Part A includes a correct answer 

Extras 

and complete work (1.5). The 

Page 4 

response to Part B includes a correct answer and complete work/explanation (1.5). 


Page 14

Annotation: a-1.0 b-1.5 = 2.5 points; Part A has the correct strategy with a computation error when dividing 432 by 3). Part 

B is correct with work based on Part A. 


Anchor 

The response to Part A includes an incorrect Page answer 3 due to a calculation error (1.0). 

The response to Part B includes a correct answer and complete work (based on 

answer to Part A) (1.5). 


Page 15

Annotation: a-1.5 b-.5 = 2.0 points; Part A is correct with work. Part B has started the strategy correctly but subtracts 36 

from 144 rather than dividing 144 by 36. 


Anchor 

The response to Part A includes a correct answer Page 4 and complete work (1.5). 

The response to Part B includes an incorrect answer but shows some correct 

procedure (0.5). 


Page 16

Annotation: a-0 b-.5 = .5 points; Part A is incorrect. Part B has some correct procedure. The student set up the problem 

correctly but then divides by 3 which is incorrect. 


Anchor 

Page 5 

The response to Part A includes an incorrect answer (0). The response to Part B 

includes an incorrect answer but shows some correct procedure (0.5). 


Page 17


Annotation: a-1.5 b-0 = 1.5 points; Part A is correct (not left if terms of pi). Part B is incorrect. 


The response to Part A includes a correct answer and complete work (1.5). No 

Anchor 

deduction was made for an answer not left in Page terms 6 of pi. The response to Part B 

includes an incorrect answer (0). 


Page 18

Nevada 

DEPARTMENT 

OF 

EDUCATION 

GRADE 

8 

Appendix II 

Administrative 

Support 


Nevada 


MATHEMATICS 


Page 19

Name: 

Answer Document 


1. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

9. 

10. 

A 

A 

A 

A 

A 

A 

A 

A 

A 

B 

B 

B 

B 

B 

B 

B 

B 

B 

C 

C 

C 

C 

C 

C 

C 

C 

C 

D 

D 

D 

D 

D 

D 

D 

D 

D 

A B C D 

11. Written Response 


Page 20

WRITTEN RESPONSE 

MATHEMATICS 

D 

O 

N 

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C 

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DO NOT WRITE IN THIS SPACE 

STOP 



MATHEMATICS 

D 

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STOP 



MATHEMATICS 

D 

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STOP 



MATHEMATICS 

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Nevada Department of Education 

Nevada 

DEPARTMENT 

OF 

EDUCATION 

James W. Guthrie 

Superintendent of Public Instruction 

Office of Assessment, Program Accountability, and Curriculum 

775-687-9188 

GRADE 

8 

CRT • Instructional Materials

Grade 8 Math Instructional Materials 2013.pdf - RPDP

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